Problem 57 Apply the appropriate property t... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 57

Apply the appropriate property to simplify the expression. $$-8+(4-p)$$

Short Answer

Expert verified

-4 - p

Step by step solution

Identify Terms Inside Parentheses

Identify the terms inside the parentheses in the expression $-8+(4-p)$. Here, the terms inside the parentheses are $4$ and $-p$.

Apply the Distributive Property

Since there is no coefficient in front of the parentheses, the distributive property allows us to remove the parentheses directly. Rewrite the expression without parentheses: $-8 + 4 - p$.

Combine Like Terms

Now combine the like terms. Here, $-8$ and $4$ are the like terms as they are both constants. Calculate $-8 + 4$:$-8 + 4 = -4$.

Write the Simplified Expression

After combining the like terms, write the simplified expression: $-4 - p$. This is the final, simplified form of the expression.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property

The distributive property is a useful tool in algebra that helps simplify expressions. It's particularly handy when dealing with parentheses. To understand how it works, we need to know the basic rule: \[ a(b + c) = ab + ac \]
This means you multiply each term inside the parentheses by the term outside them. Even if there鈥檚 no coefficient in front of the parentheses, like in the given problem, $-8+(4-p)$, the property still allows removing the parentheses easily.
It鈥檚 essential to apply this correctly to simplify expressions and solve equations effectively.

Combining Like Terms

Combining like terms is another fundamental concept in algebra. Like terms are terms that have identical variable parts. For example, in the expression \[-8 + 4 - p\], the terms $-8$ and $4$ are constants, so they are considered like terms.
To combine them, simply add or subtract their coefficients. In this case:

$-8 + 4 = -4$

This step reduces the expression into fewer terms, making it simpler and more manageable.

Parentheses in Algebra

Parentheses in algebra are used to group terms together and indicate the order of operations. When simplifying expressions with parentheses, always perform operations inside the parentheses first.
For the problem $-8+(4-p)$, recognizing that $4\text{ and }-p$ are inside the parentheses is crucial. Following the order of operations (PEMDAS/BODMAS), we simplify what's inside the parentheses before anything else. In cases where nothing inside the parentheses needs simplifying, you can treat the parentheses as a group and apply the distributive property to remove them.
This method ensures you handle all terms systematically, leading to a correctly simplified expression.

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91影视

Apply the appropriate property to simplify the expression. $$-8+(4-p)$$

Short Answer

Step by step solution

Identify Terms Inside Parentheses

Apply the Distributive Property

Combine Like Terms

Write the Simplified Expression

Key Concepts

Distributive Property

Combining Like Terms

Parentheses in Algebra

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